Space-Filling Curves for Real-Space Electronic Structure Calculations.

Hamiltonian matrices for Kohn-Sham calculations implemented in real space are often large (millions by millions) but very sparse. This poses challenges and opportunities for iterative eigensolvers, which often require a large number of matrix-vector multiplications. As a consequence, an efficient parallel sparse matrix-vector multiplication algorithm is desired. Here, we investigate the benefits of using Hilbert space-filling curves (SFCs) in domain partitioning. We show that the use of Hilbert SFCs in grid-point partitioning brings better locality of the grid points, improves balance of communication, and reduces communication overhead. We also demonstrate an extension of Hilbert SFCs coupled with blockwise operations. The use of blockwise operations helps exploit the vector-processing units in contemporary computational platforms. We illustrate speedup and scalability improvements for an iterative eigensolver based on the Chebyshev-filtered subspace iteration method. Using blockwise Hilbert SFCs, we solve the Kohn-Sham problem for silicon nanocrystals up to 10 nm in diameter, which contain over 26,000 atoms. We illustrate how the density of states of silicon nanocrystals evolves to the bulk limit, where Van Hove singularities are clearly apparent.

Probing the orbital origin of conductance oscillations in atomic chains.

We investigate periodical oscillations in the conductance of suspended Au and Pt atomic chains during elongation under mechanical stress. Analysis of conductance and shot noise measurements reveals that the oscillations are mainly related to variations in a specific conduction channel as the chain undergoes transitions between zigzag and linear atomic configurations. The calculated local electronic structure shows that the oscillations originate from varying degrees of hybridization between the atomic orbitals along the chain as a function of the zigzag angle. These variations are highly dependent on the directionally and symmetry of the relevant orbitals, in agreement with the order-of-magnitude difference between the Pt and Au oscillation amplitudes observed in experiment. Our results demonstrate that the sensitivity of conductance to structural variations can be controlled by designing atomic-scale conductors in view of the directional interactions between atomic orbitals.

Electronic level alignment at a metal-molecule interface from a short-range hybrid functional.

Hybrid functionals often exhibit a marked improvement over semi-local functionals in the description of the electronic structure of organic materials. Because short-range hybrid functionals, notably the Heyd-Scuseria-Ernzerhof (HSE) functional, can also describe the electronic structure of metals reasonably well, it is interesting to examine to which extent they can correctly describe the electronic structure at metal-organic interfaces. Here, we address this question by comparing HSE calculations with many-body perturbation theory calculations in the GW approximation, or with experimental photoemission data, for two prototypical systems: benzene on graphite and benzene diamine on gold. For both cases, we find that while HSE yields results that are somewhat closer to experiment than those of semi-local functionals, the HSE prediction is still lacking quantitatively by ∼1 eV. We show that this quantitative failure arises because HSE does not correctly capture the fundamental gap of the organic or its renormalization by the metal. These discrepancies are traced back to missing long-range exchange and correlation components, an explanation which applies to any conventional or short-range hybrid functional.

Molecules on si: electronics with chemistry.

Basic scientific interest in using a semiconducting electrode in molecule-based electronics arises from the rich electrostatic landscape presented by semiconductor interfaces. Technological interest rests on the promise that combining existing semiconductor (primarily Si) electronics with (mostly organic) molecules will result in a whole that is larger than the sum of its parts. Such a hybrid approach appears presently particularly relevant for sensors and photovoltaics. Semiconductors, especially Si, present an important experimental test-bed for assessing electronic transport behavior of molecules, because they allow varying the critical interface energetics without, to a first approximation, altering the interfacial chemistry. To investigate semiconductor-molecule electronics we need reproducible, high-yield preparations of samples that allow reliable and reproducible data collection. Only in that way can we explore how the molecule/electrode interfaces affect or even dictate charge transport, which may then provide a basis for models with predictive power.To consider these issues and questions we will, in this Progress Report, review junctions based on direct bonding of molecules to oxide-free Si.describe the possible charge transport mechanisms across such interfaces and evaluate in how far they can be quantified.investigate to what extent imperfections in the monolayer are important for transport across the monolayer.revisit the concept of energy levels in such hybrid systems.

Molecular electronics at metal/semiconductor junctions. Si inversion by sub-nanometer molecular films.

Electronic transport across n-Si-alkyl monolayer/Hg junctions is, at reverse and low forward bias, independent of alkyl chain length from 18 down to 1 or 2 carbons! This and further recent results indicate that electron transport is minority, rather than majority carrier dominated, occurs via generation and recombination, rather than (the earlier assumed) thermionic emission, and, as such, is rather insensitive to interface properties. The (m)ethyl results show that binding organic molecules directly to semiconductors provides semiconductor/metal interface control options, not accessible otherwise.